Question

10. A concave mirror forms a real image of an object placed
in front of it at a distance 30 cm, of size three times the
size of object. Find (a) the focal length of mirror
(b) position of image.
​

Answer 1

Solution:-

As per the given data,

• Object distance = - 30 cm

(Object distance is negative as distances are always measured from the pole of the mirror )

• hi = - 3ho

( The negative sign shows that the image formed is inverted  )

Magnification of the mirror is given by the formula ,

m = - (v / u ) = hi / ho

Hence ,

➝ - v / u = hi / ho

➝ - v = hi x u / ho

➝ - v = - 3 ho x - 30 / ho

➝ - v = + 90 cm

➝   v = - 90 cm

The image is formed at a distance of 60 cm on the same side as that of the object

By using mirror formula ,

➝ 1 / f = 1 / v + 1 / u

➝ 1 / f = 1 / - 90 + 1 / - 30

➝ 1 / f = - 1 /  90 - 1 /  30

➝ 1 / f = - 1 - 3 /  90  

➝ 1 / f = -4 / 90

➝ f = - 22.5 cm

The focal length of the concave mirror is - 22.5 cm